smc-666-10-Perimeter

Measurement, NAP-L3-CA32 SA

Ronald places 5 identical hexagonal tiles side-by-side to make the pattern pictured below.

Each tile has a perimeter of 24 cm and is in the shape of a regular hexagon.

What is the perimeter of the large shape, in centimetres?

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`64\ text(cm)`

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`text(Length of 1 side)`	`= 24 ÷ 6`
	`= 4\ text(cm)`

`:.\ text(Perimeter)`	`= 16 xx 4`
	`= 64\ text(cm)`

Measurement, NAP-K3-CA34

Aragorn is fencing a paddock on his property. The total length of fencing he requires is 8.2 kilometres.

The length of the paddock is 2.8 kilometres.

How wide is the paddock?

Write your answer, in kilometres to one decimal place?

kilometres

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`1.3`

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`text(Express as a perimeter equation:)`

`2 xx 2.8 + 2x`	`= 8.2`
`2x`	`= 2.6`
`:. x`	`= 1.3\ text(km)`

Measurement, NAP-K3-CA30

Sabre want to frame a square photograph that has an area of 64 square centimetres.

Sabre makes the frame using 4 strips of aluminium.

Each strip is 4 centimetres longer than the width of the photograph.

What is the total length of the 4 strips aluminium he uses to make the frame?

`text(32 cm)`	`text(40 cm)`	`text(48 cm)`	`text(56 cm)`

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`text(48 cm)`

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`text(Side length of photograph)`

`= sqrt64`

`= 8\ text(cm)`

`:.\ text(Total length of aluminium)`

`= 4 xx (8 + 4)`

`= 4 xx 12`

`= 48\ text(cm)`

Measurement, NAP-A3-NC14

What is the perimeter of this shape?

44 cm	47 cm	60 cm	146 cm

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`60\ text(cm)`

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`text{Perimeter (clockwise from top left corner)}`

`= 8 + 8 + 6 + 5 + 10 + 3 + 4 + 16`

`= 60\ text(cm)`

Measurement, NAP-A3-CA22

This shape is made from eight equilateral triangles and one large parallelogram.

Each side of all the small triangles is 4 cm long.

What is the perimeter of the shape?

`text(12 cm)`	`text(44 cm)`	`text(48 cm)`	`text(68 cm)`

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`text(48 cm)`

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`text{Perimeter from the top left corner (clockwise)}`

`=12+4+4+4+4+8+4+8`

`=48\ text(cm)`

Measurement, NAP-J3-CA34 SA

Penelope made a shape using 6 identical squares.

What is the perimeter of the shape?

centimetres

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`108`

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`text(Length of 1 side)`	`=27/3`
	`=9\ text(cm)`

`:.\ text(Perimeter)`

`= (10 xx 9) + (4 xx 4.5)`

`= 90 + 18`

`= 108\ text(cm)`

Measurement, NAP-D3-CA29 SA

Poppy draws a quadrilateral with a perimeter of 50 centimetres.

What is the maximum possible area of Poppy's quadrilateral?

square centimetres

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`156.25\ text(cm²)`

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`text(The maximum area will occur when the)`

`text(quadrilateral is a square.)`

`=>\ text(Length of side) = 50/4 = 12.5\ text(cm)`

`:.\ text(Maximum area)`	`= 12.5 xx 12.5`
	`= 156.25\ text(cm²)`

Measurement, NAP-D3-CA11

Goran made a triangle using string.

The perimeter of Goran's triangle was 16 cm.

Which of these could be the side lengths of his triangle?

	`text(4 cm, 4 cm, 8 cm)`
	`text(5 cm, 5 cm, 6 cm)`
	`text(5 cm, 3 cm, 8 cm)`
	`text(2 cm, 2 cm, 12 cm)`

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`text(5 cm, 5 cm, 6 cm)`

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`text(The sum of any two sides of a triangle)`

`text(must be longer than the third side,)`

`:.\ text(The only possible side lengths are: 5 cm, 5 cm, 6 cm)`

Measurement, NAP-D3-NC32 SA

Anthony creates a tile pattern using tiles in the shape of regular hexagons.

The perimeter of each tile is 24 cm.

He arranges them in the following way.

He keeps adding tiles in the same way until he has a row with a perimeter of 120 cm.

How many tiles are in Anthony's row?

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`7`

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`text(Perimeter of:)`

STRATEGY: Each extra tile adds 24 cm but takes away 8 cm from perimeter (net add of 16 cm).

`text(1 tile)`	`= 24\ text(cm)`
`text(2 tiles)`	`= 24 + 16 = 40\ text(cm)`
`text(3 tiles)`	`= 24 + 16 + 16 = 56\ text(cm)`
`vdots`
`text(7 tiles)`	`= 24 + (6 xx 16) = 24 + 96 = 120\ text(cm)`

Measurement, NAP-E3-NC31 SA

This triangle was made by cutting a square in half.

The perimeter of the triangle is 51.21 cm.

What is the area of the triangle?

square centimetres

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`112.5\ text(cm²)`

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`text{Triangle is isosceles (half a square).}`

`=>\ text(Length of triangle side)`

`= 1/2 xx (51.21 – 21.21)`

`= 1/2 xx 30`

`= 15\ text(cm)`

`:.\ text(Area)`	`= 1/2 bh`
	`= 1/2 xx 15 xx 15`
	`= 112.5\ text(cm²)`

Measurement, NAP-F3-CA32 SA

A square has an area of 169 square centimetres.

What is the perimeter?

centimetres

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`52`

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`text(Let)\ \ x = text(length of 1 side)`

`text(Area) = x xx x`	`= 169`
`x^2`	`= 169`
`x`	`= sqrt 169`
	`= 13\ text(cm)`

`:.\ text(Perimeter)`	`= 4 xx 13`
	`= 52\ text(cm)`

Measurement, NAP-B3-NC15 SA

A rectangular parking lot has a perimeter of 80 m.

Each short side has a length of 10 m.

What is the length of the long side?

metres

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`30`

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`text(Let)\ \ d=\ text(long side of parking lot)`

`2d + (2 xx 10)`	`=80`
`2d`	`=60`
`:. d`	`=30\ text(m)`

Measurement, NAP-F3-CA12

Michael cut a diagonal into a rectangular piece of wood.

What is the missing length?

`23\ text(cm)`	`22\ text(cm)`	`19\ text(cm)`	`17\ text(cm)`

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`22\ text(cm)`

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`text(Let)\ \ d=\ text(the unknown length)`

`d+38`	`=45 + 15`
`:. d`	`=60 – 38`
	`=22\ text(cm)`

Measurement, NAP-F3-CA06

Two sides of a triangle measure 6 cm and 12 cm.

Which one of these statements about the length of the third side is true?

	Its length is 6 cm.
	Its length is less than 6 cm.
	Its length is greater than 18 cm.
	Its length is greater than 6 cm but less than 18 cm.

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`text(Its length is greater than 6 cm but less than 18 cm.)`

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`=>\ text(One side of a triangle cannot be longer than)`

`text(the sum of the 2 other sides.)`

`=>\ text(One side of a triangle cannot be shorter than)`

`text(the difference between the other 2 sides.)`

`:.\ text(Its length is greater than 6 cm but less)`

`text(than 18 cm)`

Measurement, NAP-F3-NC32 SA

A farmer uses an existing stone wall and fencing to create a large grazing paddock for his sheep, as shown in the diagram below.

The fencing has 3-strand wiring which is also shown below.

How many kilometres of fencing will be required?

kilometres

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`5.7`

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`text(Fencing required)`

`= 3xx (450 + 200 + 150 + 500 + 600)`

`= 3 xx 1900`

`= 5.7\ text(km)`

Measurement, NAP-F3-NC23

Pablo cuts a paper rectangle in half.

He then places one half over the other to make a new shape.

What is the perimeter of Pablo's new shape?

centimetres

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`32\ text(cm)`

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`text(Perimeter of new shape)`

`= 8 + 8 + 3 + 5 + 5 + 3`

`= 32\ text(cm)`

Measurement, NAP-G3-NC29 SA

The length of this rectangle is one and a half times its height.

The perimeter of the rectangle is 40 centimetres.

What is the area of the rectangle?

square centimetres

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`96\ text(cm²)`

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`text(Let)\ \ \ x`	`=\ text(height)`
`3/2 x`	`=\ text(length)`

`2 xx (x + 3/2 x)`	`= 40`
`5x`	`= 40`
`x`	`= 8`

`:.\ text(Area)`	`= x(3/2 x)`
	`= 8 xx 12`
	`= 96\ text(cm²)`

Measurement, NAP-H3-NC24

Andrew drew a shape as pictured below.

What is the perimeter of this shape in centimetres?

`101`	`112`	`127`	`148`	`154`

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`154\ text(cm)`

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`text(Starting at the bottom left corner and)`

`text(moving clockwise:)`

`text(Perimeter)`	`= 26 + 30 + 26 + 8 + 21 + 16 + 21 + 6`
	`= 154\ text(cm)`